Market equilibria with hybrid linear-Leontief utilities

We introduce a new family of utility functions for exchange markets. This family provides a natural and “continuous” hybridization of the traditional linear and Leontief utilities and might be useful in understanding the complexity of computing and approximating market equilibria. Because this family of utility functions contains Leontief utility functions as special cases, finding approximate Arrow-Debreu equilibria with hybrid linear-Leontief utilities is PPAD-hard in general. In contrast, we show that, when the Leontief components are grouped, finite and well-conditioned, we can efficiently compute an approximate Arrow-Debreu equilibrium.

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